When is a sequential school choice system (non-)deficient?

We study sequential assignment systems in which objects are assigned to agents in multiple stages. While such systems are prevalent in real-life school choice and college admissions, Dur and Kesten (2019) show that these systems are neither non-wasteful nor straightforward in general. To overcome this negative observation, we consider a model in which the mechanism designer chooses an allocation schedule, i.e., in which stage to allocate each object, as well as the allocation mechanisms it uses within a system. Our analysis newly reveals that (i) in general, no allocation schedules avoid wastefulness/non-straightforwardness and (ii) a nonwasteful/straightforward allocation schedule exists if and only if the preference domain is "tiered." This result supports practices in which the tiered domain naturally arises (e.g., Chinese college admissions practice). However, this also highlights the difficulty of sequential assignments in more diverse preference domains.